QuestionAugust 19, 2025

Question 2(Multiple Choice Worth 3 points) (Continuously Compounded Interest MC) A college student plans to take out a 6,000 loan to cover the cost of purchasing a used car. If the Ioan has a 6% annual interest rate compounded continuously, with no payments due for the first two years. The student will pay off the loan with a lump sum after 15 months . Determine how much interest will be owed if the student pays off the loan after 15 months. 565.05 467.30 8,757.62 6,467.30

Question 2(Multiple Choice Worth 3 points) (Continuously Compounded Interest MC) A college student plans to take out a 6,000 loan to cover the cost of purchasing a used car. If the Ioan has a 6% annual interest rate compounded continuously, with no payments due for the first two years. The student will pay off the loan with a lump sum after 15 months . Determine how much interest will be owed if the student pays off the loan after 15 months. 565.05 467.30 8,757.62 6,467.30
Question 2(Multiple Choice Worth 3 points)
(Continuously Compounded Interest MC)
A college student plans to take out a 6,000 loan to
cover the cost of purchasing a used car. If the Ioan has
a 6%  annual interest rate compounded continuously,
with no payments due for the first two years. The
student will pay off the loan with a lump sum after 15
months . Determine how much interest will be owed if
the student pays off the loan after 15 months.
 565.05
 467.30
 8,757.62
 6,467.30

Solution
4.6(295 votes)

Answer

\467.30 Explanation 1. Identify the formula for continuously compounded interest Use A = Pe^{rt}, where P is the principal amount, r is the annual interest rate, and t is the time in years. 2. Convert months to years 15 months is \frac{15}{12} years. 3. Calculate the total amount after 15 months Substitute P = 6000, r = 0.06, and t = \frac{15}{12} into the formula: A = 6000 \cdot e^{0.06 \cdot \frac{15}{12}}. 4. Calculate the interest owed Interest = Total Amount - Principal = A - 6000.

Explanation

1. Identify the formula for continuously compounded interest<br /> Use $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years.<br />2. Convert months to years<br /> 15 months is $\frac{15}{12}$ years.<br />3. Calculate the total amount after 15 months<br /> Substitute $P = 6000$, $r = 0.06$, and $t = \frac{15}{12}$ into the formula: $A = 6000 \cdot e^{0.06 \cdot \frac{15}{12}}$.<br />4. Calculate the interest owed<br /> Interest = Total Amount - Principal = $A - 6000$.
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